How to model a mesh of curved axe?
The shape is very organic. Sculpting will let you explore the shape the fastest. You can quickly establish creases and surface curvatures and change them without much effort to your liking.

Once you are happy with the form, retopologize it into your final mesh. You have 3 options:


low poly mesh with baked normal/displacement map
low poly with subsurface modifier with creasing
low poly with subsurface modifier with control loops


If you would be experienced sub-d modeler, I believe you could model the shapes on the fly. But sculpting is easy and fast and it will help you, because the surface will be well defined and you will know better where the edge-loops go and how the topology needs to be.